NEW YORK — Every Red Sox fan knows Ted Williams hit a home run in his final at-bat in the big leagues. The ball was struck in the bottom of the eighth inning on Sept. 28, 1960 against Orioles righthander Jack Fisher.

John Updike was in the Fenway Park stands that day and was inspired to write “Hub Fans Bid Kid Adieu,’’ perhaps the most renowned sports essay of all time.

What you probably don’t know is that the Red Sox had three more games on the schedule, in New York, after Williams’s farewell blast. Williams didn’t go with his teammates to Yankee Stadium. The Sox were already 29 games out of first place and nobody seemed to mind him finishing on a high note.

All of which brings us to Derek Sanderson Jeter, the 40-year-old captain of the New York Yankees, who plans to hang up his spikes at the end of the season.

The Yankees play their final home game against the Orioles Thursday, Sept. 25. And then they finish their season in Boston with three games against the Red Sox. Any chance Jeter would pull a Ted if the Yankees are out of playoff contention?

I’ve been thinking about this for weeks and finally got a chance to ask the man as he sat at his locker before Tuesday night’s series opener with the moribund Red Sox at Yankee Stadium.

So what about it, Derek: “If the Yankees are eliminated from postseason play by Sept. 25, is it possible you won’t play the games in Boston?’’

Ever-polite, Jeter put up his hand and stopped me in mid-question.

“I don’t deal in hypotheticals,’’ he said.

Fair enough. Let’s try it another way.

“If you’re healthy, will you play the games in Boston?’’

“Why would I not?’’ he answered.

That seems clear enough. Jeter will play in Boston. He will be the same guy he has been for 20 seasons. He will honor his team and Major League Baseball. He will not do anything that would compromise the integrity of the game.

Still, I wanted to talk to him about the legend of Ted.

“Do you know what Ted did in his last game?’’ I asked.

“He hit a home run, right?’’ answered Jeter.

Right. But there were some circumstances that were unusual. Williams’s homer cut a Sox deficit to 4-3. Williams was sent out to left field for the ninth inning, then replaced by Carroll Hardy. The Sox rallied in the bottom of the inning. Willie Tasby wound up batting with the bases loaded and one out, and the Sox won the game when Baltimore’s infield butchered a double play grounder.

If Tasby walked in that at-bat, Williams would have been due up with the bases loaded in a 4-4 game. But he’d already been lifted. The game had been compromised.

A decade later, in his official autobiography with John Underwood, Williams claimed the decision to blow off the Yankee series was made before the final Fenway game:

“The team still had a doubleheader in New York that weekend, but I went to [manager Mike] Higgins and said, ‘Mike this is the last game I’m going to play. I don’t want to go to New York.’ “He said, ‘All right, you don’t have to go.’ Regardless of what I had done, this was it, I’d had it.’’

Other versions are less clear. Leigh Montville’s biography on Williams claims that as soon as Williams hit the home run vs. Baltimore, “The Red Sox quickly passed out word in the press box that Williams would not be going to New York.’’

According to the late Roy Mumpton of the Worcester Telegram, Williams had told some writers that he wanted to go out with a homer. Mumpton told Ed Linn, another Williams biographer, “If he hadn’t hit the home run, he would have gone on to New York. I’m sure of that.’’

In his 1961 book on Williams (“The Eternal Kid”), Linn wrote, “The official Red Sox line was that it had been understood all along that Ted would not be going to New York unless the pennant race was still alive. The fact of the matter, of course, is that Williams made the decision himself, and he did not make it until after he had hit the home run.’’

Linn claimed Williams’s equipment bag was packed for the trip to the Big Apple.

“I remember it all very well,’’ said veteran New York Daily News baseball columnist Jack O’Connell. “I was 12 years old and my uncle, Bill Gallagher — he was a New York City cop — he had tickets for Friday night against the Red Sox at Yankee Stadium. We were going to see Ted Williams. But he didn’t play.’’

Jeter would never do this. It would fly in the face of everything his career has stood for. Right?

“I can’t even think about that,’’ said the Yankee captain. “I’ve gone my entire career without answering hypotheticals. I don’t like jinxing anything. I’m playing today.’’

That sounds as if he’s leaving some wiggle room for not coming to Boston.

“I’m not leaving any wiggle room,’’ he said. “I’ve never spoken on a hypothetical in my entire career. My job is playing the game today, Sept. 2. That’s the game I’m playing.’’

Does he understand why Williams did what he did?

“Yeah, I understand it,’’ said Jeter. “Mo didn’t pitch in Houston last year [the Yankees played meaningless games in Houston after Mariano Rivera said goodbye to the fans at Yankee Stadium].

“It depends on the situation, I guess. I don’t know what Ted’s situation was and I didn’t know him well enough to comment on it.

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